This follows from

If you wish to see why 'P(A1 n A2) + P(A1 n A3) + P(A2 n A3) - P(A1 n A2 n A3) is positive'

draw a Venn diagram http://www.learnnc.org/reference/Venn%20diagram

The triple intersection is contained repeatedly in those other probabilities.

Note that if then .

This comes from .